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Find the values of a & b so that x^4+x^3+8x^2+ax+b,is exactly divisible by x^2+1

Posted by Mahima Pandit 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

If {tex}x^4+x^3+8x^2+ax +b{/tex} is exactly divisible by x² + 1, the remainder after division should be zero.
Now let us perform long division

We get, remainder = x (a - 1) + (b - 7)
x (a - 1) + (b - 7 ) = 0
{tex}\Rightarrow{/tex} x (a - 1) + (b - 7) = 0x + 0
{tex}\Rightarrow{/tex} a - 1 = 0 and b - 7 = 0 [On equating the coefficients of like powers of x]
{tex}\Rightarrow{/tex}a = 1 and b = 7

0Thank You

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CBSE > Class 10 > Mathematics